m1

Mathematics

GCSE Mathematics is comprised of 6 strands; number, algebra, geometry and measures, statistics, ratio and rates of change, and probability. Our curriculum is designed to develop students’ mastery of core mathematics skills during year 7 to 9 whilst promoting problem solving skills throughout all five years to meet the requirements of the new GCSE.

m2

In years 10 & 11, students on course to attain the highest grades in Set 1 will also work towards achieving a Level 2 Certificate in Further Mathematics. This course acts as a bridge between GCSE and A-Level mathematics, but is also particularly relevant for students wishing to study physics, engineering and computing (amongst other subjects) in further education. Students can also choose to study Statistics as one of their option subjects in years 10 & 11.

Areas of Study

Autumn Term Spring Term Summer Term
Year 7 Standard

 

 

Numbers and the number system

Calculating

Calculating: division

Visualising and constructing

Investigating properties of shapes

Algebraic proficiency: using formulae

 

Exploring fractions, decimals and percentages

Proportional reasoning

Pattern sniffing

Measuring space

Investigating angles

 

Calculating fractions, decimals, and percentages

Solving equations and inequalities

Calculating space

Checking approximating and estimating

Mathematical movement

Presentation of data

Measuring data

Year 8 Standard / Year 7 Higher

 

 

Numbers and the number system

Counting and comparing

Calculating

Visualising and constructing

Investigating properties of shapes

Algebraic proficiency: tinkering

Exploring fractions, decimals and percentages

Proportional reasoning

Pattern sniffing

Measuring space

Investigating angles

Calculating fractions, decimals and percentages

Solving equations and inequalities

Calculating space

Checking approximating and estimating

Mathematical movement

Presentation of data

Measuring data

 

Year 8 Higher

 

 

Number and the number system

Calculating

Visualising and constructing

Understanding risk 1

Algebraic proficiency: tinkering

 

Exploring fractions, decimals and percentages

Proportional reasoning

Pattern sniffing

Investigating angles

Calculating fractions, decimals and percentages

Solving equations and inequalities

Calculating space

Algebraic proficiency: visualising

Understanding risk 2

Presentation of data

Measuring data

 

 

Year 9 Standard Number and the number system

Calculating

Visualising and constructing

Understanding risk 1

Algebraic proficiency: tinkering

Exploring fractions, decimals and percentages

Proportional reasoning

Pattern sniffing

Investigating angles

Calculating fractions, decimals and percentages

Solving equations and inequalities

Calculating space

Algebraic proficiency: visualising

Understanding risk 2

Presentation of data

Measuring data

COMMENCEMENT OF GCSE SYLLABUS

 

Number 1:

LCM, HCF, product of prime factors

 

Algebra 1:

Algebraic Expressions including substitution, expansion and factorisation

 

Geometry & Measures 1:

Angles including parallel lines, bearings & polygons

 

Data Handling 1:

Averages and range including stem & leaf diagrams

Year 9 Higher Calculating

Visualising and constructing

Algebraic proficiency: tinkering

Pattern sniffing

Solving equations and inequalities 1

Calculating space

Conjecturing

Algebraic proficiency: visualising

Solving equations and inequalities 2

Understanding risk

Presentation of data

COMMENCEMENT OF GCSE SYLLABUS

Number 1: multiples, factors, primes, laws of indices (including fraction and negative), standard form, surds

Algebra 1: expressions – substitution, expansion, factorising, algebraic fractions

Geometry and Measures 1: angles in parallel lines, polygons, bearings, circle theorems

Data Handling 1: statistics including data collection / sampling, averages and range including grouped data, scatter diagrams, time series

Year 10 (Foundation)

 

Number 2: decimals including estimation, upper and lower bounds

Geometry and Measures 2: 2D shapes – area and perimeter including parts of a circle (arc, sector, segment)

Algebra 2: solve equations including quadratics

Number 3: Fractions

Geometry and Measures 3: Transformation (including fraction scale factor), symmetry, similar shapes

Algebra 3: formulae including substitution, change of subject, distinguish equation / formula / expression / identity

Number 4: percentages including use of multiplier, compound interest

Data Handling 2: presenting data including pie chart, scatter diagram, frequency polygon, time series

 

Geometry and Measures 4: volume and surface area of 3D shapes including sphere and pyramids

Algebra 4: sequences including geometric, nth term of linear sequence

Number 5: ratio and proportion (direct and inverse)

Algebra 5: algebraic graphs – linear, quadratic, cubic and reciprocal

 

Year 10

(Higher)

 

 

Number 2: fractions and decimals including upper and lower bounds calculations

Geometry and Measures 2: 2D shapes – area and perimeter including parts of a circle (arc, sector, segment)

Algebra 2: linear equations and graphs including algebraic and graphical solutions of simultaneous equations

Number 3: percentages including use of multiplier (exponential growth and decay), reverse percentages

Geometry and Measures 3: Transformations including negative and fractional scale factor enlargement

Algebra 3: formulae and sequences – substitution and transpose formulae, nth term of linear and quadratic sequences

Geometry and Measures 4: trigonometry 1 including Pythagoras and 3D shapes

Data Handling 2: Statistics 2 including cumulative frequency, box plots, and histograms

Geometry and Measures 5: 3D shapes – surface area and volume of prisms, pyramids, spheres, and the frustum

 

Algebra 4: algebraic graphs including quadratic, cubic, reciprocal, exponential

Number 4: ratio and proportion including direct and inverse proportion, and graphs

Geometry and Measures 6: Loci, construction and congruence

Algebra 5: Inequalities including graphical solutions

Data Handling 3: Probability

 

Year 11 (Foundation)

 

Number 5:

Ratio & Proportion (direct and inverse)

 

Algebra 5

Algebraic Graphs- linear, quadratic, cubic and reciprocal

 

Geometry & Measure 5

Measure inc compound; conversion of measure, graphs

 

Algebra 6

Inequalities- notation, on a line, solve

 

Number 6

Powers & Roots inc rules for indices & standard form

 

Geometry & Measure 6

Pythagoras Theorem and Trigonometry

Data Handling 3:

Probability

 

Geometry & Measure:

Constructions   Loci Congruence

 

Algebra 7:

Solve Simultaneous Equations – algebraic & graphical methods

 

Algebra 8:

Vector Geometry

 

PREPARATION FOR THE GCSE EXAMINATIONS- MODIFIED SYLLABUS BASED ON MOCK ANALYSIS
Year 11

(Higher)

 

 

Number 4:

Ratio & Proportion inc direct & inverse & graphs

 

Geometry & Measure 6:

Loci, Constructions & Congruence

 

Algebra 5:

Inequalities inc graphical solutions

 

Data Handling 3:

Probability

 

Algebra 6:

Further Factorising Quadratics inc complete the square; Manipulate & simplify algebraic fractions

 

Geometry & Measure 7:

Trigonometry 2 inc sine/cosine rule, trig graphs, area formula

Algebra 7:

Solve Quadratic Equations inc factorising, completing square, formula; Equations with fractions

 

Geometry & Measure 8:

Similar Shapes inc length, area and volume

 

Algebra 8:

Simultaneous Equations -linear/quadratic equations; Equation of circle; Equation of tangent

 

Geometry & Measures 9:

Vectors in solve geometric problems

 

Algebra 9:

Transformation of   Functions inc trigonometric graphs

PREPARATION FOR THE GCSE EXAMINATIONS- MODIFIED SYLLABUS BASED ON MOCK ANALYSIS

Assessment

Students in years 7 to 9 will be assessed throughout the year through the use of fortnightly maths tracker tests, online Firefly quizzes and year GCSE-style termly examinations. Beginning in year 9 until the end of year 11students are assessed using end of unit assessments and GCSE papers. Progress is also informed by class work and homework.

Firefly/Extended Learning

Extended learning activities are set as according to the school policy, through the school’s virtual learning environment (VLE) Firefly. This way all tasks can be viewed by students and their parents/carers. We encourage daily use of Firefly with students regularly clearing completed tasks on the ‘Your Tasks’ section of their profile to maintain good organisation.

In addition to this Firefly also contains useful information and support material. Details about equipment, suitable calculators and assessment dates are kept up to date on the Mathematics pages. A range of practise examination papers, tutorial videos on different topics and a student moderated forum section are also available.

Exam Specifications

AQA GCSE Mathematics Specification

AQA GCSE Statistics Specification

AQA Level 2 Further Mathematics Specification

 

Online Resources

MyMaths – An online resource for all students to access for reference, practise and homework purposes. Students all have a personal login that enables them to keep a record of their progress across topics throughout their time at Trentham.

TTRockstars – TTRockstars (Times Table Rockstars) is an online system designed to support students in learning their times tables, vital for progress in a wide range of mathematic topics.

BBC Bitesize – Student resources for revising mathematics.

Apps

iMathematics – A tool for reference and practise purposes, particularly for number, algebra and geometry topics.

Minds of Modern Mathematics – An app that details practical applications and the historical developments made in the field of mathematics.

MyScript Calculator – A handwriting calculator particularly useful for developing understanding of the order of operations and mathematical syntax.

Calculator for iPad – A free calculator to make up for the absence of an existing one.

Geometry Pad – An app for creating interactive diagrams to assist in understanding a range of geometry topics.

Quick Graph – An app for plotting graphs from an equation.

Extra –curricular activities

  • Year 11 mock examination preparation (end of Autumn term)
  • Year 11 GCSE preparation (Summer term)
  • Homework club in AW1 (one lunchtime per week – see student briefing)
  • Chess club (weekly – see student briefing)

 

Statistics

Statistics is the branch of mathematics that deals with the collection, analysis and interpretation of data. In studying statistics, a wide range of job opportunities are available. A statistician may:

  • Consult in the design, analysis and evaluation of clinical studies for pharmaceutical companies
  • Design experiments for agricultural, ecological, environmental or energy-related studies
  • Investigate mortality and accident rates for insurance companies
  • Derive opinion polls for a public relations firm or television network
  • Work with psychologists to develop theories relating to learning and behaviour
  • Evaluate the performance of combinations of chemicals in industry
  • Conduct reliability and quality control evaluations in a variety of industries
  • Develop time series and forecasting models for different socio-economic sections of society

m2m1

 

Areas of Study

In years 7 to 9 statistics is studied as part of the main provision for mathematics (see information on mathematics curriculum)

Autumn Term Spring Term Summer Term
Year 10 Planning a strategy

Data collection: types of data, obtaining data, census data, sampling, conducting a survey/experiment

Tabulation for ungrouped and grouped data

Graphs for qualitative data (pie charts and comparative pie charts)

Graphs for qualitative data (pie charts and comparative pie charts)

Graphs for quantitative discrete data (vertical line graphs)

Graphs for quantitative continuous data (frequency polygons, population pyramids, histograms with equal and unequal class intervals)

Measures of averages (arithmetic mean, geometric mean, median, mode, and estimates from grouped data)

Measures of spread (range, quartiles, inter-quartile range, inter-decile and inter-percentile range, standard deviation and variance, types of distribution, normal distribution, skew, and standardised scores)

Year 11 Cumulative frequency curves and polygons, and box and whisker plot (drawing, estimating median, quartiles, IQR, deciles, inter-decile range and percentiles)Scatter graphs (plotting, drawing line of best fit using double-mean point, correlation, Spearman’s correlation coefficient, interpreting Product Moment correlation coefficient, interpolation and extrapolation, calculation of the equation of the line of best fit)

Time series (graph, moving averages, trend line, seasonal effect, z-charts, output gap charts

Remaining calculations and graphing methods (chloropleth maps, transforming data from one presentation to another, index number, chain base numbers, RPI, CPI, crude rates and standardised rates)

Probability (compound events, sample space diagrams, Venn diagrams, tree diagrams, conditional probability, expected frequencies)

Controlled Assessment

Revision and time to cover topics identified as weaker areas from Y11 mock examination

Assessment

During formal assessment periods during year 10 and year 11, students will complete a past paper examination. Each term throughout year 10, and the autumn term of year 11, students will complete a practise controlled assessment. Teachers will also use end of unit assessment and homework to track progress.

Firefly/Extended Learning

Extended learning activities are set as according to the school policy, through the school’s virtual learning environment (VLE) Firefly. This way all tasks can be viewed by students and their parents/carers. We encourage daily use of Firefly with students regularly clearing completed tasks on the ‘Your Tasks’ section of their profile to maintain good organisation.

In addition to this Firefly also contains useful information and support material. Details about equipment, suitable calculators and assessment dates are kept up to date on the Mathematics pages.

Links to useful Resources/ Exam Specifications/ Apps

AQA GCSE Statistics Specification (4310)

MyMaths – An online resource for all students to access for reference, practise and homework purposes. Students all have a personal login that enables them to keep a record of their progress across topics throughout their time at Trentham. There is a dedicated area on GCSE statistics within the website.

BBC Bitesize – Student resources for revising mathematics.

Minds of Modern Mathematics – An app that details practical applications and the historical developments made in the field of mathematics.

MyScript Calculator – A handwriting calculator particularly useful for developing understanding of the order of operations and mathematical syntax.

Calculator for iPad – A free calculator to make up for the absence of an existing one.

Quick Graph – An app for plotting graphs from an equation.

Extra –curricular activities

  • Year 11 mock examination preparation (end of Autumn term)
  • Year 11 GCSE preparation (Summer term)
  • Homework club in AW1 (one lunchtime per week – see student briefing)